the panel board appears to be... a Murray Catalogue # LC130DC: Model 19 Type 1 enclosure, Type F panelboard with a 100 amp main breaker (service disconnect) inside the panel at the top.
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The outlets, other than kitchen and bathroom, are for two-pronged plugs (no ground hole), but the outlet boxes read as grounded at all but two of these outlets. I've been cautioned not to assume this is a machine ground and to be cautious about plugging heavy equipment or large appliances into these.
....buy a non-contact voltage detector, shut off the service disconnect......
If this goes well, maybe I'll consider adding a couple more circuits and replacing the accessible sheathed cable in the basement. Second floor and first floor ceiling stuff, I think I leave to someone with more experience.
I'm all good to go on fishing wire and installing the new box under the window for the a/c. I just need to get my act together on the breaker.
A Murray panel is excellent news: absolutely the most common, solid and readily available panel and breakers. Cheap too. And you have plenty of room, there is no issue of it being a sub panel which can trip up the newbie.
A master disconnect. Seriously. Once you flip that off, you really need to be attempting suicide to end up deceased. This is as modern and as reliable a bit of hardware as you are going to find. Once you flip that to the off position, the buss bars that the breakers hang on will be de-energized. The non-contact tester is an excellent idea.
You can certainly consider fitting three prong outlets where you find a ground. Spend a few dollars: buy the better equipment. Receptacles can be bought all day long for 17 cents each. And they are utter junk. If the receptacles you are considering are costing you $1.50 or so, you are likely buying solid stuff. A clue is the yolk. That is the metal strap at which it is screwed to the box. If it passes all the way behind the receptacle, rather than passing into it at about half its depth, it is likely a good unit.
Even better, but likely part of this sort of receptacle, is it having a bronze spring on one of the screws that ties it to the box. The code used to permit a receptacle to be considered grounded if it just had two screws going thru the yolk (into a metal box). Now it either must have the spring I describe (it is a flat thing) or a wire from the grounding screw to a legitimate ground in the box.
Another aspect of the better receptacles that I like a lot: one does not wrap the wire around the screw. There is a flat plate behind which the bare wire, straight, is inserted, and then the screw torques down on that. I absolutely prefer these and have no problem getting clients to pay the slight (as a fraction of the entire project) cost of the upgrade. Just hold the two in your hands and you will see my point.
If you are going to replace receptacles at all, learn what a multi wire circuit is. They present hazards if not understood, but are easy to understand, if you understand me. Ask and I will tell you more. The point comes down to being careful how you work the neutral, if you have multi-wire circuits in the house.
Anywhere you do not have a ground, you can install a GFI to be assured there is no problem.
Why are you adding circuits? Do you feel an actual need for them? Are you intending to make more use of the basement, such as having a wood working shop down there?
If none of your breakers are tripping in the use that you are putting them to, you probably don't need more circuits.
Having a few more outlets is a different question.